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Old 2022-02-05, 17:59   #9
Jan 2017

100110012 Posts

Originally Posted by Dr Sardonicus View Post
It occurred to me to wonder how many times the block of decimal digits representing a prime p can reasonably be expected to occur before it occurs in its proper place in the sequence of primes.
Each sequence of n digits should occur equally often. Thus if you sequentially search for 50 6-digit sequences, you should on average expect to have seen 50 of the last sequence - on average encountering it once before finding each of the earlier 49 ones.

So the expected number should be (number of earlier equally long target sequences) + (number of one earlier one digit shorter target sequences)/10 + (two shorter)/100 and so on.
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